Similar Issue, Phone Won't Power On :(

I bought my S3 new on ebay, it has worked like a gem for over a month. Last night the battery died before I had a chance to plug it in to charge, since then I can't get it to power on. When I take the battery out and plug it in all I get is a red LED for maybe 10 seconds then nothing. I've tried charging it and the battery gets hot so I know something is working. I have it plugged in without the battery now, tried the volume up, power and home button for maybe 30 seconds but nothing. It's doesn't vibrate, buzz, blink, etc. Nothing, nada. I don't know anything about software, firmware or whatever. I just know that I can't get the phone to come on, no matter what has been previously suggested.

I got the S3 when the charge port broke on my S2. Do I just have bad luck with the Samsung Galaxy brand or is this common? lol

This is NOT common, but it might be related to the same thing: The charging port. If it broke inside or moved around, some power pins might be touching each other or touching wires that they shouldn't, making your phone act all weird and potentially shorting out stuff that might be dangerous. Also, if I recall correctly, your phone cannot power on without a battery inside, so that might explain why trying to boot into Recovery mode with just the charger is not doing squat.

Try doing the same but with the battery inside. Does your phone show ANY signs of life?

I didn't mean that I tried to reboot without the battery, I meant that I tried all of those things. The only sign of life is that the battery gets hot after it's plugged in for a while and the random red LED when I first plug it in WITHOUT the battery.

Then I would try two things:
1) If you have a friend with an S3, try your battery in theirs. Does it work? Bad news for you. It doesn't? Now try their battery in yours; it should work then.
2) If it doesn't work, just take it in for Warranty replacement or repairs if you're not covered. The battery getting hot could indicate a short circuit somewhere, but it could be inside the battery or it could be something inside the phone.